In practice, it probably makes no difference which one you use. OpenJDK and the Oracle (not Sun!) badged JDK are based on the common OpenJDK code base. The biggest difference in practice (IMO) is that patches seem to arrive earlier for the Oracle branded version than for the OpenJDK-based packages in typical Linux distros.
Which one would have the most support?
I you want support for Java, contact Oracle sales and they can arrange a support contract. As part of that, they will advise you on which they can provide better support for.
In practice, it probably makes no difference which one you use. OpenJDK and the Oracle (not Sun!) badged JDK are based on the common OpenJDK code base. The biggest difference in practice (IMO) is that patches seem to arrive earlier for the Oracle branded version than for the OpenJDK-based packages in typical Linux distros.
I you want support for Java, contact Oracle sales and they can arrange a support contract. As part of that, they will advise you on which they can provide better support for.